{"paper":{"title":"5-Point 1PI Proper Vertex Function of Gluon and the S-Matrix Element","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","nucl-th"],"primary_cat":"hep-ph","authors_text":"Gouranga C Nayak","submitted_at":"2017-05-08T15:47:52Z","abstract_excerpt":"As far as the renormalization in perturbative QCD is concerned the n-point one particle irreducible (1PI) proper vertex function is the basic building block where the ultra-violet (UV) divergence occurs when the loop momentum integration limit goes to infinity. In this paper we express the S-matrix element for the $gg \\rightarrow ggg$ scattering process at all orders in coupling constant in terms of 5-point, 4-point, 3-point 1PI proper vertex functions and the (full) propagator by using the path integral formulation of QCD."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02927","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}